Allan Franklin (Colorado), “The Rise and Fall of the Fifth Force”
In 1986 Ephraim Fischbach, Sam Aronson, and Carrick Talmadge proposed a modification of Newton’s Law of Universal Gravitation. This modification changed the gravitational potential from V = -Gm₁m₂/r² to V =
(-Gm₁m₂/r²) [1 + α e^-r/λ] where α, the strength of the interaction, was approximately one percent and the range of the force λ was approximately 100 meters. This additional term was known as the Fifth Force. This suggestion was based on tantalizing evidence provided by a reanalysis of the Eötvös experiment, an early test of the Equivalence Principle, a difference between the measured value of G, the gravitational constant, as determined by laboratory measurements and those performed in mineshafts, and a small energy dependence in the CP-violating parameters in K^o meson decay. The two initial measurements of the Fifth Force disagreed. One supported its existence and the other did not. How this discrepancy was resolved and the subsequent history of experiments on the Fifth Force will be discussed. By 1990 the consensus was that such a Fifth Force did not exist.

Helge Kragh (Aarhus), “Continual Fascination: Oscillatory Cosmological Models after Einstein”
The idea of an oscillatory or cyclical universe has roots far back in time, and within the context of general relativity it was reconsidered by Friedmann in 1922-23 and Einstein in 1931. During the subsequent decades, this kind of model was not highly regarded, and yet it was found attractive by pioneer cosmologists such as Lemaître, Gamow and Bonnor. The model continued to attract attention, in part for ideological and other non-scientific reasons. It was developed in a variety of versions, all the way up to the string-based Steinhardt-Turok model proposed in 2002. This paper offers a survey of cyclical models in the post-1917 era and seeks to explain the continual fascination of such models. Particular attention will be paid to the early period between 1920 and 1960 and to the motives of proposing this kind of model of the universe.

Dan Kennefick (Fayetteville, Arkansas), “Relativistic Lighthouses: The role of binary pulsars in proving the existence of gravitational waves”
Theory testing is considered a key role for experiment, but the requirements for an experiment to really discriminate between theories are so narrow that it may be that theory testing by an individual experiment rarely happens. For instance experimenters need to have predictions of theories, and this requires theorists to perform calculations to make those predictions. But what if the calculations are challenged on theoretical grounds? This was the scenario facing the astronomers measuring the orbital decay of the first binary pulsar, which was thought to be due to gravitational radiation reaction. For decades controversy had persisted amongst theorists over whether the prediction of general relativity (the quadrupole formula) was properly established as a prediction of that theory. In essence the role played by this experiment would not just be to test the theory, but to point the theorists in the direction of the correct calculation. This paper examines how the experimenters and theorists responded to this situation, including examining the role played by alterative theories and the ways in which the theory testing paradigm may be used to permit experimenters to comment upon theoretical controversies without appearing to involved themselves directly.

Christopher Smeenk (London, Ontario), “Inflation as a Theory of Structure Formation”
Inflationary cosmology has remained the dominant research paradigm in early universe cosmology over the last 30 years largely due to its success in accounting for the spectrum of primordial density perturbations. My talk has two main aims. The first is to consider the account of structure formation given by inflation in its historical context, both in terms of its introduction and later refinement, and via comparison with a competing account of structure formation that was the main rival of inflationary cosmology through the 90s, namely structure formation due to topological defects. Precision observations of temperature anisotropies in the CMBR have ruled out the most plausible model s of structure formation via defects, but these observations are compatible with inflationary models. Second, to what degree does this success support inflationary cosmology? Here I will consider two objections to the claim that CMBR observations provide strong support for inflation: (1) are the successful predictions of inflation distinctive? (2) does inflationary cosmology merely accommodate observational results by adjusting parameters of the model, rather than giving successful predictions?

Abhay Ashtekar (Penn State), “Classical Singularities and Quantum Spacetime”
At space-time singularities, general relativity breaks down. They are thus gates to new physics beyond Einstein. I will review the deep puzzles and apparent paradoxes that singularities lead to, then recall attempts at resolution of these puzzles and of the singularities themselves, and finally summarize the recent advances that have emerged from quantum geometry

Jörg Frauendiener (New Zealand), “Development and applications of conformal infinity”
The notion of conformal infinity is a very useful geometric abstraction of the asymptotic regions of a space-time. In this talk a discussion of the development of this notion will be given from its early beginnings to the present day status. Some applications of conformal infinity ranging from quantisation to numerical simulations will be presented.

Roger Penrose (Oxford), “Conformal boundaries, Quantum Geometry, and Cyclic Cosmology”
For nearly half a century, the notion of a conformal boundary has proved itself to be a useful mathematical tool for the treatment of the remote futures or pasts of space-times models. In accordance with a proposal by Tod, a plausible characterization of the extremely special nature of the Big Bang is that this singularity can be described as a conformal boundary where the space-time conformal geometry extends smoothly to a region prior to it. Conformal Cyclic Cosmology (CCC) takes this region seriously and identifies it with the remote future of a previous universe “aeon”. CCC contrasts the “wild” quantum geometry relevant to black-hole singularities to the conformally smooth Big Bang, whose classical singularity is taken to reside entirely in the conformal factor.

Norbert Straumann (Zürich), “Problems with modified theories of gravity, as alternatives to dark energy”
Since no satisfactory explanation of dark energy has emerged so far, it is certainly reasonable to investigate whether possible modifications of GR might change the late expansion rate of the universe. After all, GR has not yet been tested on cosmological scales. In my brief review I shall mainly concentrate on the simplest modification, so called ƒ(R) gravity, but the status of some other attempts will also be discussed.

Hans Jörg Fahr (Bonn), “Cosmologies with cosmic vacuum energy decay and the creation of effective cosmic matter”
Cosmic vacuum energy has by now taken on a nearly unassailable role in modern cosmology. The cosmological constant Λ -- invented by Einstein, but later also rejected by him -- presently celebrates its fantastic resurrection, and in the framework of present day “precision cosmology” it helps to conciliate observational data with theoretical predictions. In the general relativistic field equations the term connected with Λ acts the same way as a constant vacuum energy density would: if positive, it has an accelerating action on cosmic dynamics. We, however, want to show that the concept of a constant vacuum energy density is unsatisfactory for very basic reasons, one being that it would constitute a physical reality that acts upon spacetime and matter dynamics without itself being acted upon by spacetime or matter. Looking into the cosmological literature of the past, one finds various mechanisms for cosmic mass generation. It is interesting to observe that various, theoretically described forms of mass generation in the universe lead to terms in the field equations which are, in many respects, analogous to, or can even be replaced by, terms arising from vacuum energy. We will also point to other cosmological literature where it is demonstrated that gravitational cosmic binding energy acts as a form of negative cosmic mass energy, and this again leads to terms similar to those written for cosmic vacuum energy. These studies thus show that the cosmic actions of vacuum energy, gravitational binding energy, and mass creation are evidently closely related to each other. Based on these results we shall suggest that the action of vacuum energy on cosmic spacetime inevitably leads to a decay of vacuum energy density, a decrease of cosmic binding energy, and the creation of effective mass in the expanding universe. We demonstrate that under these auspices only an expanding universe with constant total energy, the so-called economic universe, should be possible in which both cosmic mass density and cosmic vacuum energy density are decreasing according to (1/S²), S being the characteristic scale of the universe. Only under these conditions does the origin of the present universe from an initially pure cosmic vacuum state appear to be possible. This is because the incredibly huge vacuum energy density, derived by quantum field theoreticians for an economic universe during its expansion to present-day scales, has decayed to the small value consistent with observations in the present universe, but its energy reappears in the energy density of created effective cosmic matter.

Erhard Scholz (Wuppertal), “Can scale covariant Weylian geometry be relevant in contemporary cosmology?”
For integrable scale connections the Weyl-geometric scale gauge stands in close relationship to conformal geometry and field theory. It allows a “pseudo-conformal” deformation of the metric (“pseudo” because the affine connection is unaffected by Weyl-geometric re-scalings) and an adaptation of certain aspects of conformal field theory, in particular those of scalar fields, to Weylian geometry. In this talk a geometrically very simple class of cosmological models in the pseudo-conformal setting will be presented and discussed (“Weyl universes”). They seem to be consistent with the findings of observational cosmology (cosmological redshift, microwave background, supernovae magnitude-redshift characteristic, quasar data etc.). If considered as a potentially realistic candidate for cosmological geometry, some of the deeply entrenched convictions of the expanding world cosmologies of the 20^th century are put into question (in particular the view of a real space expansion, the physical existence of an initial singularity and its immediate physical implications). These aspects of present standard cosmology might then turn out to be theoretical artifacts of an improperly chosen gauge (the Riemann-Einstein gauge).

Sergiu Klainerman (Princeton): On Cosmic Censorship and the Cauchy Problem

Donal O’Shea (Mt. Holyoke, Mass.), “The Unexpected Resolution of the Poincaré Conjecture”
In six papers over the decade beginning in 1895, Henri Poincaré created algebraic topology and used it to study manifolds of dimension three and four. In the last paragraph of the last page of the last of these great topological papers, he stated a conjectural characterization of the three-dimensional sphere that became known simply as the Poincaré Conjecture. The conjecture resisted all attempts to settle it for over a century, and it became the most famous problem in topology. Just recently, the conjecture received a stunning proof by Grigori Perelman. I describe the conjecture and the two profound ironies that lie at the heart of its resolution. Its statement is purely topological, and almost everyone expected that any resolution would come from topology. However, the proof depends crucially on geometry and, more precisely, William Thurston’s notion that three-dimensional manifolds are composed of regions that carry unique geometric structures. The first irony is that Poincare's apprehension, and ultimately proof, of the same phenomenon for two-dimensional manifolds guided his intuition and propelled him to fame. But neither he, nor anyone else (until 1980), imagined that an analogous result might hold for three-dimensional manifolds. The second irony is that the Poincaré conjecture is the simplest question that one could ask of a pre-relativistic model of the universe, but the its proof depends critically on the equations arising in general relativity. More precisely, establishing that three-dimensional manifolds carry geometric structures depends on endowing them with a riemannian metric (easy), and analyzing the Ricci flow (hard). The Ricci flow is governed by precisely the same equations that Einstein considered on four-dimensional manifolds modeled on space-time without the cosmological constant, and the considerations that led Einstein to the equations are the same that led Richard Hamilton and Perelman to use it in the context of three manifolds. A third, as yet unrealized, irony is that Perelman’s topologically-motivated work on the Ricci flow may lead well beyond Einstein to far-reaching new insights in general relativity.

Domenico Giulini (MPI für Gravitationsphysik, Golm), “On the Nature of Geometrodynamics”
Einstein's field equations of General Relativity can be written as evolution equations for the geometry of space geometrodynamics). I review this approach and point out various mathematical problems (mostly topological) associated with it, some of which directly relate to the theory of 3-manifolds. Some of the answers to these problems give rise to intriguing speculations on the possible physical relevance of the topology of space.

Robert Wald (Chicago): On Quantum Field Theory in Curved Spacetimes

Matthias Gaberdiel (Zurich): String Theory and Spacetime Geometry
String Theory appears to define a quantum theory of gravity. I shall attempt to explain how, from the point of view of string theory, spacetime geometry emerges, and to which extent this is captured by concepts of classical geometry.

Jürg Fröhlich (Zurich): Events in Quantum Theory and the Emergence of Space-Time